A novel adaptive importance sampling algorithm based on Markov chain and low-discrepancy sequence

A novel adaptive importance sampling method is proposed to estimate the structural failure probability. It properly utilizes Markov chain algorithm to form an adaptive importance sampling procedure. The main concept is suggesting the proposal distributions of Markov chain as the importance sampling density. Markov chain states can adaptively populate the important failure regions thus the importance sampling based on them will yield an efficient and accurate estimate of the failure probability. Compared with existent methods, it does not need the solution of the design point(s) or the pre-sampling in the failure region. Various examples are given to demonstrate the advantages of the proposed method.